This cuboid is made from 6 small cubes,
Write how many small cubes there are in this cuboid

Answer:

Grams of Peanuts = 52.5

Grams of Raisins = 210

Step-by-step explanation:

14/4 = 3.5

21/6 = 3.5

30/5 = 3.5

3.5 · 15 = 52.5

3.5 · 60 = 210

Notice that

11/12 = 1/6 + 3/4

so that

tan(11π/12) = tan(π/6 + 3π/4)

Then recalling that

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

⇒   tan(x + y) = (tan(x) + tan(y))/(1 - tan(x) tan(y))

it follows that

tan(11π/12) = (tan(π/6) + tan(3π/4))/(1 - tan(π/6) tan(3π/4))

tan(11π/12) = (1/√3 - 1)/(1 + 1/√3)

tan(11π/12) = (1 - √3)/(√3 + 1)

tan(11π/12) = - (√3 - 1)²/((√3 + 1) (√3 - 1))

tan(11π/12) = - (4 - 2√3)/2

tan(11π/12) = - (2 - √3) … … … [A]

The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.

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The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

14 = 14

Step-by-step explanation:

(4 + 2) + 8 = 14

6 + 8 = 14

14 = 14

The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer:

667.38

Step-by-step explanation:

28,000 loan amount

4 years

6.76%

Answer:

a.

$567.27

Step-by-step explanation:

Edge 2020

The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 500

p = 0.58

q = 1 - 0.58 = 0.42

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96

Therefore, the margin of error of the population proportion estimation for a 95% confidence interval is

1.96√(0.58)(0.42)/500 = 0.043

Answer:

rhombus

Step-by-step explanation:

Answer:

rhombus

Step-by-step explanation:

A rhombus has four congruent sides, and does not necessarily have to have right angles. (A square is considered a rhombus and has four right angles, so that is the only exception). So, your answer would be rhombus!

Hope this helped! ;)

The area of the square is given by the  quadratic expression:

\(A = 9x^2 - 6xy + y^2\)

If we have a square whose side measures S, the area of said square is given by the equation:

\(A = S^2\)

In this case, we know that the side length of our square is given by:

\(S = 3x - y\)

Replacing that in the area equation we get:

\(A = (3x - y)^2\)

Now we just need to expand that product, we will get:

\(A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2\)

Then we can see that the correct option is the last one.

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Applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

The tangent to a circle theorem states that if a line is tangent to a circle, then it will be perpendicular to the radius of the circle.

The two tangents theorem states that two tangents that intersect at a point outside a circle are equal in length.

Applying the tangent to a circle theorem, ΔWXO would be a right triangle. Therefore, apply Pythagorean theorem to find XW given the following:

OX=3.2

OW = 6.8

Applying the pythagroean theorem, we would have:

XW = √(OW² - OX²)

Substitute

XW = √(6.8² - 3.2²)

XW = 6

Based on the two tangents theorem, XW = WY. Therefore,

WY = 6.

In summary, applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

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Answer:

616.2442

area to the nearest whole number=616

Step-by-step explanation:

using formula 1/2absinx

where a =44,b=29 ,x=105

1/2x44x29xsin105

44x29=1276

1276÷2=638

638 x sin 105

the sin of 105 is 0.9659

if u are using a four figure table where u can't find 105 under sin of angle

u simply subtract 105 from 180=75

638 x 0.9659 =616.2442

approx.616

The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

From the question, we have the following parameters that can be used in our computation:

First = tan(θ)

Second = cos(θ)

The basis trigonometry identity is

sin²(θ) + cos²(θ) = 1

Divide through the equation by cos²(θ)

So, we have

tan²(θ) + 1 = 1/cos²(θ)

Subtract 1 from both sides

tan²(θ) = - 1 + 1/cos²(θ)

Take the square root of both sides

tan(θ) = √[-1 + 1/cos²(θ)]

Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:

Sam spent 33 dollars on baseball gear

Step-by-step explanation:

1. he has 64 dollars

2. he is left with 31 dollars

3. 64 - 31 = 33

2. you can check by adding 31+33=64

The company needs to sell 50 phones a week to break even.

The formula for finding the breakeven point is:

= Fixed costs / Contribution margin

The Contribution margin is found by deducting the variable costs from the selling price.

Variable cost = $350 per phone

Fixed cost = $25,000 incurred per week

Contribution margin :

= Selling price - variable cost

= 850 - 350

= $500

Breakeven point:

= 25,000 / 500

= 50 phones

50 phones need to be sold weekly for the company to break even.

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The answer for it is diagram B because it does not cross or have parallel lines

The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

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324309

doctors were registered that year.

Explanation:

The questions says, "18.1% of all registered doctors are females"

(Consider, total number of registered doctors as

x

)

that's,

18.1

%

of

x

are female.

and

18.1

%

of

x

is

58

,

700

.

Mathematically,

18.1

100

⋅

x

=

58700

x

=

58700

⋅

100

18.1

x

=

324309

doctors were registered that year.

Using the arc length formula, the length of the outer curve is approximately 85 feet.

Arc length = ∅/360 × 2πr.

Apply the arc length formula to find the length of the outer curve, given the following:

Plug in the values

Arc length = 70/360 × 2(3.14)(70)

Arc length = 70/360 × 2(3.14)(70) ≈ 85 feet.

The length of the outer curve is approximately 85 feet.

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The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

Given:

Radius (r) = 20 inches

Height (h) = 0.7 feet

First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:

Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches

Now, we can substitute the values into the volume formula:

Volume = π * (20 inches)^2 * 8.4 inches

Calculating the volume:

Volume = 3.14159 * (20 inches)^2 * 8.4 inches

≈ 3.14159 * 400 inches^2 * 8.4 inches

≈ 1005.3096 cubic inches

Rounding the volume to the nearest tenth:

Volume ≈ 1005.3 cubic inches

Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

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Answer:

C

Step-by-step explanation:

if we consider perfect squares either side of 45 , that is

36 < 45 < 49 , then

\(\sqrt{36}\) < \(\sqrt{45}\) < \(\sqrt{49}\) , so

6 < \(\sqrt{45}\) < 7

thus \(\sqrt{45}\) is between 6 and 7 , that is point C on the number line

Answer:

C

Explanation:

√45 is irrational, so to approximate where it goes on the number line, you should find the closest squares to it, which are 36 and 49. These numbers are the squares of 6 and 7, so √45 can't be A, B, or D, as none of them are between 6 and 7. Only C is, and as √45 is closer to √49 than √36, it should be closer to 7 in the number line, but still in between both of them.

Hope this helps !! :D

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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Answer: Option(C) is correct option

Explanation:

Margin of error is the factor that occurs in survey for determining random sampling error. It indicates about confidence interval (CI) through describing difference occurring in poll result and actual population value.If there is high margin of error, then confidence is low because poll result will not reflect the actual population result collected through survey.

According to the question, researcher would try to get small margin of error so that lower confidence interval can be acceptable because large confidence interval(CI) will indicate more margin of error.

Other options are incorrect because small margin of error cannot produce increment in confidence or usage of large confidence.Large confidence interval will result in large margin of error. Thus, the correct option is option(c).

Answer:

A

Step-by-step explanation:

I did the math and i have no doubt

The value of trigonometric function tan θ = -1 is θ = 3π/4.

What are trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

The given function is tan θ = -1.

θ = tan^-1(-1)

θ = π- tan ^-1(1)

θ = π- π/4

θ = 3π/4

Therefore, the value is obtained as θ = 3π/4.

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After analyzing, it can be concluded that the functions f and g are:

A. f(0) is larger than g(0).

B. f(3) is larger than g(3).

To determine which of the two functions is larger at any given point, one must compare the heights of the two functions at the same point on the x-axis. At point x=0, the height of the f(x) function is larger than the height of the g(x) function, so f(0) is larger than g(0).

Similarly, at point x=3, the height of the f(x) function is larger than the height of the g(x) function, so f(3) is larger than g(3).

To compare which of two functions is larger at any given point, we need to compare the heights of the two functions at the same point on the x-axis. For example, at x=0, the height of the f(x) function is larger than the height of the g(x) function, so f(0) is larger than g(0). The same comparison can be made at any other point on the x-axis.

For example, at x=3, the height of the f(x) function is larger than the height of the g(x) function, so f(3) is larger than g(3). This comparison can be done for any point on the x-axis, which will allow us to determine which of the two functions is larger at any given point.

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